Live mathematical reference

Mathematical compendium

A live index of the equations in published articles. Each entry leads to its article, equation guide, and the terms explained there. New or edited published articles appear automatically.

1680 equations across 1484 symbols.

J(θ)=Ex∼D, y∼πθ(⋅∣x)[r(x,y)]−βDKL(πθ(⋅∣x) ∥ πref(⋅∣x))J(\theta) = \mathbb{E}_{x \sim \mathcal{D},\ y \sim \pi_\theta(\cdot \mid x)}\left[r(x,y)\right] - \beta D_{\mathrm{KL}}\left(\pi_\theta(\cdot \mid x) \,\|\, \pi_{\mathrm{ref}}(\cdot \mid x)\right)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Ltotal≈Lretrieve+k⋅ℓrerank+LgenerateL_{\mathrm{total}} \approx L_{\mathrm{retrieve}} + k \cdot \ell_{\mathrm{rerank}} + L_{\mathrm{generate}}

1 published occurrence

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This equation gives an approximation: it relates the quantities while allowing an approximation.

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Ltotal=Lenc+∑i=1k(Lretrieve(i)+LLLM(i))L_{\text{total}} = L_{\text{enc}} + \sum_{i=1}^{k} \left( L_{\text{retrieve}}^{(i)} + L_{\text{LLM}}^{(i)} \right)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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P(correct)  =  P(R) P(correct∣R)⏟grounded in retrieved evidence  +  P(¬R) P(correct∣¬R)⏟correct without sufficient retrieved evidenceP(\text{correct}) \;=\; \underbrace{P(R)\,P(\text{correct} \mid R)}_{\text{grounded in retrieved evidence}} \;+\; \underbrace{P(\lnot R)\,P(\text{correct} \mid \lnot R)}_{\text{correct without sufficient retrieved evidence}}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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p(y∣x)≈∑z∈Zk(x)pη(z∣x) pθ(y∣x,z)p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\, p_\theta(y \mid x, z)

1 published occurrence

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This equation gives an approximation: it relates the quantities while allowing an approximation.

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p(y∣x)≈∑z∈top-k(pη(⋅∣x))pη(z∣x) pθ(y∣x,z)p(y \mid x) \approx \sum_{z \in \mathrm{top}\text{-}k\left(p_\eta(\cdot \mid x)\right)} p_\eta(z \mid x) \, p_\theta(y \mid x, z)

1 published occurrence

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This equation gives an approximation: it relates the quantities while allowing an approximation.

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Renterprise=Rmodel+Rplatform+RapplicationR_{\mathrm{enterprise}} = R_{\mathrm{model}} + R_{\mathrm{platform}} + R_{\mathrm{application}}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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